A simplified mathematical model for the dam-breach hydrograph for three reservoir geometries following a sudden full dam break

Abstract

The prediction of dam-break water flow at dam site is essential to reduce the potential for loss of damage in the downstream floodplain. In this study, the influence of reservoir shapes (rectangular, trapezoidal and triangular wedge) on dam-break discharge hydrographs at a dam site was investigated to estimate the peak discharge and discharge hydrograph quickly. By assuming instantaneous and complete breaches to simplify the discharge process, a formula for the peak discharge and a simple analytical solution to the entire discharge hydrograph following a dam break at the dam site were generated. The discharge hydrograph at the dam site derived by the proposed mathematical model was validated through a comparison with the results calculated by the numerical simulation and other existing approaches. The outflow discharges calculated by both the mathematical and numerical model was very similar under the conditions of the three different reservoir shapes. The overall discharge hydrograph shape was mainly influenced by the length of the reservoir, while the magnitude of the outflow discharge was primarily affected by the initial water depth.

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Acknowledgements

This research was supported financially by the State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, China (Grant No. 2017ZZKT-5), the National Natural Science Foundation of China (Grant No. 51609197), CAS “Light of West China” Program (Grant No. XAB2016AW06) and the Xian Science and Technology Program (Grant No. SF1335).

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Correspondence to Tao Li.

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Hu, H., Zhang, J., Li, T. et al. A simplified mathematical model for the dam-breach hydrograph for three reservoir geometries following a sudden full dam break. Nat Hazards 102, 1515–1540 (2020). https://doi.org/10.1007/s11069-020-03979-w

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Keywords

  • Instantaneous dam break
  • Peak discharge
  • Discharge hydrograph
  • Reservoir shape
  • A simple analytical solution